BCJ identities and d-dimensional generalized unitarity

Abstract

We present a set of relations between one-loop integral coefficients for dimensionally regulated QCD amplitudes. Within dimensional regularization, the combined use of color-kinematics duality and integrand reduction yields the existence of relations between the integrand residues of partial amplitudes with different orderings of the external particles. These relations can be established for the cut-constructible contributions as well for the ones responsible for rational terms. Starting from the general parametrization of one-loop residues and applying Laurent expansion in order to extract the coefficients of the amplitude decomposition in terms of master integrals, we show that the full set of relations can be obtained by considering the BCJ identities between d-dimensional tree-level amplitudes. We provide explicit examples for multi-gluon scattering amplitudes at one loop.

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

“…(3.40) or (3.41), the β function of the fdf-scalar coupling to fermions is finally given by 42) and therefore identical to the renormalization of the evanescent coupling in fdh for e e = e, compare with Eq. (2.8b).…”

“…The use of dimensionally regularized tree-amplitudes within fdf has been employed to study the colour-kinematics duality [41] for one-loop dimensionally regularized amplitudes [42]. The extension of fdf beyond the one-loop level is currently under investigation.…”

Light-like scattering in quantum gravity

“…The consequence of the monodromy BCJ relations for one-loop integral coefficients have been studied in [45] and [46], while a string theory based systematic derivation of these relations was given in [47].…”

From Jacobi off-shell currents to integral relations

“…Similarly, new relations at oneloop level have been found with a clever use of the BCJ relations with string theory [24][25][26][27][28] and unitarity based methods [29,30].…”